These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Any of the rock tracks that start up. With Bart, that's expected. But with unexpected characters like Marge, Lisa and Apu, you know they're getting serious.
Special mention goes to 'Never Trust A Snake', which makes up for it being really difficult.
Crazy Awesome: Some of the vehicles, such as Apu's Monster Truck and the RC Car.
Hilarious in Hindsight: Remember the South Park gag "Simpsons did it!" By the time you get to the game's final levels it turns out the plot is remarkably similar to an episode of South Park, namely that Earth is being recorded by aliens to sell as a reality show to the galaxy. The really funny part though is that the South Park episode came first, in March 2003, while Hit & Run came out in September. And for extra irony, the "Simpsons did it!" episode came out just the previous year; one must wonder if the producers of the two shows planned this out for the timing to be so perfect.
No Problem with Licensed Games: A shining example. The voice actors are right from the cartoon and are still funny in their roles, the story is ridiculously enjoyable (emphasis on ridiculous), and so much Continuity Porn that any diehard fan will go nuts over it.
That One Level: The final three missions, which force you to drive perfectly and avoid so much as lightly hitting anything if you don't want to knock off the extremely sensitive barrel of nuclear waste strapped to your fender. Worse still is that the last two contain a chase sequence which will absolutely cause you to fail if you can't outrun it on the first pass.
'Never Trust A Snake', from the fifth level. Simply put, you will not get it on the first try. The main problem is that, in the second part of the mission where you're collecting trash on foot, the time you have left after doing it becomes the time you have to get back to the DMV (a pretty substantial distance away). Which is very jarring, since usually a whole new timer is given for getting to the final destination. The second time around, you can get it without significant hassle if you plan your route carefully, but it still takes some shortcut use on the expressway.
Also of notable mention is 'Set To Kill', the penultimate mission of the sixth level. It takes some very skilful driving and knowledge of the map to hit all of the laser stands with even a few seconds left on the clock, and also a fair amount of luck when you factor in traffic. The trip back to Krustylu is even worse, giving you only fifty seconds to get there from the opposite side of the map. You need to go flat-out and pray to God you don't suffer any major hold-ups, otherwise you're guaranteed to not make it. Even with the Globex Super Villain Car, it's damned tough.
The reedeeming feature about the above two missions is that they are both backed by the same very awesome rock track noted above, arguably one of the best in the game. So if you keep failing, it also means to get plenty of time to listen to the music!
'Kwik Cash', the level that comes after 'Never Trust a Snake'. Your mission is to destroy an armored car.... with Snake's Li'l Bandit. Fortunaly, the only time limit you have is to go to Googolplex and escape Chief Wiggum twice (First at the end of the freeway and the last at the Snake's Hideout.). There's no time limit to destroy the armored car because it takes forever to destroy the toughest vehicle in the game with a sports car.